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Linear Regression with Multiple Regressors

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. Econometrics Mind Map on Linear Regression with Multiple Regressors, created by ioanabendris on 13/06/2015.
ioanabendris
Mind Map by ioanabendris, updated more than 1 year ago
ioanabendris
Created by ioanabendris almost 10 years ago
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Resource summary

Linear Regression with Multiple Regressors
  1. Omitted Variable Bias
    1. Omitted factor W must be:
      1. Determinant of Y
        1. Correlated with the regressor x
        2. OLS estimator is biased and inconsistent
          1. Formula to get bias
            1. Solutions
              1. Run a randomized controlled experiment
                1. Adopt "cross tabulation" approach
                  1. Include omitted variable: multiple regression
                2. Multiple Regression Model
                  1. Interpretation of coefficients
                    1. Get BAD
                  2. OLS estimator
                    1. Beta1Small vs. Beta1Large
                    2. Measures of Fit
                      1. R
                        1. SER
                          1. R adjusted
                          2. LSA for Multiple Regression
                            1. Conditional Mean Zero
                              1. Omitted variable
                                1. Belongs in equation (is in U)
                                  1. Correlated with an included X
                                2. i.i.d.
                                  1. X and Y have finite 4th moments
                                    1. No perfect multicolinearity
                                      1. One of the regressors is an exact linear function of the other regressors
                                    2. Control variable vs. Variable of Interest
                                      1. Conditional Mean Independence
                                        1. Implications
                                          1. OLS estimator beta1hatlarge is unbiased and consistent
                                            1. betawhat is not consistent and not meaningful
                                              1. Usual inference methods apply to beta1hatlarge
                                          2. Sampling Distribution of the OLS estimator
                                            1. Multicollinearity and Dummy Variable Trap
                                              1. Perfect Multicollinearity
                                                1. One of the regressors is an exact linear function of the other regressors
                                                2. Dummy Variable Trap
                                                  1. When happens?
                                                    1. Full set of binary variables and an intercept are included
                                                    2. Solutions?
                                                      1. Omit one of the groups
                                                        1. Omit the intercept
                                                      2. Imperfect Multicollinearity
                                                        1. 2 or more regressors are highly correlated
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